Nassar boarded the plane at Detroit Metro Wayne County Airport in freezing Michigan temperatures -- the fact he didn't get a jacket makes us smile.

Records show the flight lasted 4 hours and 36 minutes. Nassar appears to be shackled and surrounded by law enforcement officials ... so we're guessing it wasn't exactly a Paris Hilton style private jet flight.

We asked the Federal Bureau of Prisons if it's typical for a high-profile prisoner to fly private but only got this response: "Due to security reasons, we do not share information on methods of prisoner transportation."

The good news ... Nassar has begun his 60-year sentence for child pornography crimes in a high-security federal prison in Tucson -- with roughly 1,500 other inmates.

His release date is scheduled for March 23, 2069 -- but he'll probably be dead by then.